It seems plausible that general training in things like “what to do when you’re stuck on a problem”, “how to use your network to effectively find solutions”, “when & how to ask for help”, “how to stay motivated even when you’re lost”, “how to lead meetings with your research mentors”, and “how to generally take care of your mental health” could be useful.

IMO interesting to note is that it is my impression that these are among the main things you learn in an AI PhD, or at least things you would encounter and have to deal with (The transferable skills, which are in addition to the technical skills).
I would bet this is a big part of "being a good researcher".
Writing this as someone who isn't doing an AI PhD.